Problem: Simplify the following expression: $\sqrt{48} - \sqrt{27}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{48} - \sqrt{27}$ $= \sqrt{16 \cdot 3} - \sqrt{9 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{3} - \sqrt{9} \cdot \sqrt{3}$ $= 4\sqrt{3} - 3\sqrt{3}$ Finally, simplify by combining the terms. $= ( 4 - 3 )\sqrt{3} = \sqrt{3}$